scholarly journals Mean equicontinuity and mean sensitivity on cellular automata

2020 ◽  
pp. 1-18
Author(s):  
LUGUIS DE LOS SANTOS BAÑOS ◽  
FELIPE GARCíA-RAMOS
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
The Other ◽  
Other Hand ◽  
Full Shift ◽  
Mean Sensitivity

Abstract We show that a cellular automaton (or shift-endomorphism) on a transitive subshift is either almost equicontinuous or sensitive. On the other hand, we construct a cellular automaton on a full shift (hence a transitive subshift) that is neither almost mean equicontinuous nor mean sensitive.

Assessing the Utilization of Automata in Representing Players' Behaviors in Game Theory

Game Theory ◽  
2017 ◽  
pp. 106-119
Author(s):  
Khaled Suwais
Keyword(s):  
Game Theory ◽  
Cellular Automata ◽  
Finite Automata ◽  
The State ◽  
The Other ◽  
Direct Impact ◽  
Complex Environments ◽  
Other Hand ◽  
Different Types ◽  
State Of Art

Representing players' strategies in game theory has a direct impact on the players' performance. The state of art shows that automata are one of the primary techniques used for representing players' strategies and behaviors. In this paper, the author will identify different types of automata and assess their utilization in the field of game theory. Is has been found that finite automata, adaptive automata, and cellular automata are widely adopted in game theory. The utilization of finite automata is found to be limited to represent simpler players' behavior. On the other hand, adaptive automata and cellular automata are intensively applied in complex environments, where the number of interacted players is large and therefore, representing complex behaviors are needed.

scholarly journals When is a dynamical system mean sensitive?

2017 ◽  
Vol 39 (06) ◽  
pp. 1608-1636 ◽  
Author(s):  
FELIPE GARCÍA-RAMOS ◽  
JIE LI ◽  
RUIFENG ZHANG
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
The Other ◽  
Positive Entropy ◽  
Topological Dynamical System ◽  
Other Hand ◽  
Open Question ◽  
Uniquely Ergodic ◽  
Mean Sensitivity ◽  
Transitive System

This article is devoted to studying which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things, we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive. On the other hand, we provide an example of a transitive system which is cofinitely sensitive or Devaney chaotic with positive entropy but fails to be mean sensitive. As applications of our theory and examples, we negatively answer an open question regarding equicontinuity/sensitivity dichotomies raised by Tu, we introduce and present results of locally mean equicontinuous systems and we show that mean sensitivity of the induced hyperspace does not imply that of the phase space.

scholarly journals Causal influence in operational probabilistic theories

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 515
Author(s):  
Paolo Perinotti
Keyword(s):  
Quantum Theory ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Classical Theory ◽  
The Other ◽  
Causal Influence ◽  
Causal Networks ◽  
A Cell ◽  
Reversible Evolution ◽  
Probabilistic Theories

We study the relation of causal influence between input systems of a reversible evolution and its output systems, in the context of operational probabilistic theories. We analyse two different definitions that are borrowed from the literature on quantum theory—where they are equivalent. One is the notion based on signalling, and the other one is the notion used to define the neighbourhood of a cell in a quantum cellular automaton. The latter definition, that we adopt in the general scenario, turns out to be strictly weaker than the former: it is possible for a system to have causal influence on another one without signalling to it. Remarkably, the counterexample comes from classical theory, where the proposed notion of causal influence determines a redefinition of the neighbourhood of a cell in cellular automata. We stress that, according to our definition, it is impossible anyway to have causal influence in the absence of an interaction, e.g. in a Bell-like scenario. We study various conditions for causal influence, and introduce the feature that we call no interaction without disturbance, under which we prove that signalling and causal influence coincide. The proposed definition has interesting consequences on the analysis of causal networks, and leads to a revision of the notion of neighbourhood for classical cellular automata, clarifying a puzzle regarding their quantisation that apparently makes the neighbourhood larger than the original one.

String Generation by Cellular Automata

2021 ◽  
Vol 30 (2) ◽  
pp. 111-132
Author(s):  
Martin Kutrib ◽  
◽  
Andreas Malcher ◽  
Keyword(s):  
Cellular Automata ◽  
Real Time ◽  
Structural Properties ◽  
The Other ◽  
Time Constraints ◽  
Closure Properties ◽  
Other Hand ◽  
The One

In contrast to many investigations of cellular automata with regard to their ability to accept inputs under certain time constraints, in this paper we are studying cellular automata with regard to their ability to generate strings in real time. Structural properties such as speedup results and closure properties are investigated. On the one hand, constructions for the closure under intersection, reversal and length-preserving homomorphism are presented, whereas on the other hand the nonclosure under union, complementation and arbitrary homomorphism are obtained. Finally, decidability questions such as emptiness, finiteness, equivalence, inclusion, regularity and context-freeness are addressed.

scholarly journals Limit sets of stable cellular automata

2013 ◽  
Vol 35 (3) ◽  
pp. 673-690 ◽  
Author(s):  
ALEXIS BALLIER
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Point Of View ◽  
Limit Set ◽  
Limit Sets ◽  
Sofic Shift ◽  
Almost Everywhere ◽  
Sofic Shifts ◽  
Full Shift ◽  
Factor Map

AbstractWe study limit sets of stable cellular automata from a symbolic dynamics point of view, where they are a special case of sofic shifts admitting a steady epimorphism. We prove that there exists a right-closing almost-everywhere steady factor map from one irreducible sofic shift onto another one if and only if there exists such a map from the domain onto the minimal right-resolving cover of the image. We define right-continuing almost-everywhere steady maps, and prove that there exists such a steady map between two sofic shifts if and only if there exists a factor map from the domain onto the minimal right-resolving cover of the image. To translate this into terms of cellular automata, a sofic shift can be the limit set of a stable cellular automaton with a right-closing almost-everywhere dynamics onto its limit set if and only if it is the factor of a full shift and there exists a right-closing almost-everywhere factor map from the sofic shift onto its minimal right-resolving cover. A sofic shift can be the limit set of a stable cellular automaton reaching its limit set with a right-continuing almost-everywhere factor map if and only if it is the factor of a full shift and there exists a factor map from the sofic shift onto its minimal right-resolving cover. Finally, as a consequence of the previous results, we provide a characterization of the almost of finite type shifts (AFT) in terms of a property of steady maps that have them as range.

scholarly journals A Graph-Transformational Approach to Swarm Computation

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 453
Author(s):  
Larbi Abdenebaoui ◽  
Hans-Jörg Kreowski ◽  
Sabine Kuske
Keyword(s):  
Cellular Automata ◽  
Graph Transformation ◽  
Ant Colony ◽  
The Other ◽  
Mathematical Basis ◽  
Particle Swarms ◽  
Other Hand ◽  
Pheromone Trails ◽  
Graph Class ◽  
And Control

In this paper, we propose a graph-transformational approach to swarm computation that is flexible enough to cover various existing notions of swarms and swarm computation, and it provides a mathematical basis for the analysis of swarms with respect to their correct behavior and efficiency. A graph transformational swarm consists of members of some kinds. They are modeled by graph transformation units providing rules and control conditions to specify the capability of members and kinds. The swarm members act on an environment—represented by a graph—by applying their rules in parallel. Moreover, a swarm has a cooperation condition to coordinate the simultaneous actions of the swarm members and two graph class expressions to specify the initial environments on one hand and to fix the goal on the other hand. Semantically, a swarm runs from an initial environment to one that fulfills the goal by a sequence of simultaneous actions of all its members. As main results, we show that cellular automata and particle swarms can be simulated by graph-transformational swarms. Moreover, we give an illustrative example of a simple ant colony the ants of which forage for food choosing their tracks randomly based on pheromone trails.

MODELING EPIDEMIC BASED ON PENNA MODEL

2005 ◽  
Vol 16 (05) ◽  
pp. 799-805 ◽  
Author(s):  
MINGFENG HE ◽  
QIUHUI PAN ◽  
BINGLIN YU
Keyword(s):  
Cellular Automata ◽  
Infection Rate ◽  
Death Rate ◽  
Two Dimensions ◽  
The Other ◽  
Initial Ratio ◽  
Cellular Automata Model ◽  
Inherited Diseases ◽  
Other Hand ◽  
Penna Model

A cellular automata model is developed aiming to study the epidemic on a lattice of two dimensions. The characteristics of individual including reproduction, death by inherited diseases and age are studied in the Penna model. The spreading of epidemic and the reproduction of individual are considered as cellular automata. We shall mainly discuss the influence on the number of epidemical patients by infection rate and death rate. The results show that the existence of epidemic mainly depends on the infection rate and the death rate but not the initial ratio of patients. There are two reasons for nonexistent epidemic. As long as the infection rate is less than 0.3, the epidemic cannot spread. On the other hand, if the infection rate and the death rate are both high, the individuals with epidemic die out and the epidemic cannot spread, either. The epidemic can exist all along when the combination of infection rate and death rate are in the mid area.

On surjunctive monoids

2015 ◽  
Vol 25 (04) ◽  
pp. 567-606 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Michel Coornaert
Keyword(s):  
Cellular Automata ◽  
The Other ◽  
Finite Alphabet ◽  
Finitely Generated ◽  
Commutative Monoids ◽  
Residually Finite ◽  
Finite Monoids ◽  
Other Hand ◽  
Bicyclic Monoid

A monoid M is called surjunctive if every injective cellular automata with finite alphabet over M is surjective. We show that all finite monoids, all finitely generated commutative monoids, all cancellative commutative monoids, all residually finite monoids, all finitely generated linear monoids, and all cancellative one-sided amenable monoids are surjunctive. We also prove that every limit of marked surjunctive monoids is itself surjunctive. On the other hand, we show that the bicyclic monoid and, more generally, all monoids containing a submonoid isomorphic to the bicyclic monoid are non-surjunctive.

Assessing the Utilization of Automata in Representing Players' Behaviors in Game Theory

2014 ◽  
Vol 6 (2) ◽  
pp. 1-14 ◽  
Author(s):  
Khaled Suwais
Keyword(s):  
Game Theory ◽  
Cellular Automata ◽  
Finite Automata ◽  
The State ◽  
The Other ◽  
Direct Impact ◽  
Complex Environments ◽  
Other Hand ◽  
Different Types ◽  
State Of Art

Representing players' strategies in game theory has a direct impact on the players' performance. The state of art shows that automata are one of the primary techniques used for representing players' strategies and behaviors. In this paper, the author will identify different types of automata and assess their utilization in the field of game theory. Is has been found that finite automata, adaptive automata, and cellular automata are widely adopted in game theory. The utilization of finite automata is found to be limited to represent simpler players' behavior. On the other hand, adaptive automata and cellular automata are intensively applied in complex environments, where the number of interacted players is large and therefore, representing complex behaviors are needed.

scholarly journals Shifts with decidable language and non-computable entropy

2008 ◽  
Vol Vol. 10 no. 3 (Automata, Logic and Semantics) ◽  
Author(s):  
Peter Hertling ◽  
Christoph Spandl
Keyword(s):  
Real Number ◽  
Topological Entropy ◽  
Polynomial Time ◽  
The Other ◽  
Other Hand ◽  
Enumerable Language ◽  
International Audience ◽  
Full Shift ◽  
The One ◽  
Infinite Sequences

Automata, Logic and Semantics International audience We consider subshifts of the full shift of all binary bi-infinite sequences. On the one hand, the topological entropy of any subshift with computably co-enumerable language is a right-computable real number between 0 and 1. We show that, on the other hand, any right-computable real number between 0 and 1, whether computable or not, is the entropy of some subshift with even polynomial time decidable language. In addition, we show that computability of the entropy of a subshift does not imply any kind of computability of the language of the subshift

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